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Circle Mensuration

In the follow...

Question

In the following figure, three semicircle of diameters $A B = 8 c m, B C = 4 c m$ and $C D = 2 c m$ are drawn. Find the length of the boundary of a shaded portion. $(Take π = \frac{22}{7})$ .

36 c m

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22 c m

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12 c m

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72 c m

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Solution

The correct option is A $36 c m$
Circumference of semi-circle $= d + \frac{π d}{2}$
Length of boundary of shaded portion $= 8 + \frac{π (8)}{2} + 4 + \frac{π (4)}{2} + 2 + \frac{π (2)}{2}$
$= 14 + 7 π$
$= 14 + 7 \times \frac{22}{7}$
$= 36 c m$

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and

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In the following figure, three semicircle of diameters AB=8 cm,BC=4 cm and CD=2 cm are drawn. Find the length of the boundary of a shaded portion. (Take π=227).

The correct option is A 36 cmCircumference of semi-circle =d+πd2Length of boundary of shaded portion =8+π(8)2+4+π(4)2+2+π(2)2=14+7π=14+7×227=36 cm

In the following figure, three semicircle of diameters $A B = 8 c m, B C = 4 c m$ and $C D = 2 c m$ are drawn. Find the length of the boundary of a shaded portion. $(Take π = \frac{22}{7})$ .

The correct option is A $36 c m$
Circumference of semi-circle $= d + \frac{π d}{2}$
Length of boundary of shaded portion $= 8 + \frac{π (8)}{2} + 4 + \frac{π (4)}{2} + 2 + \frac{π (2)}{2}$
$= 14 + 7 π$
$= 14 + 7 \times \frac{22}{7}$
$= 36 c m$